Space & Depth Perception
Lecture 11. Thurs, 10/08
Jonathan Pillow
Perception (PSY 323), Fall 2009
The University of Texas at Austin
Hans Holbein
The Ambassadors
1533
“Anamorphosis”
Color Constancy (follow-up from last time)
Color Constancy (follow-up from last time)
Depth Perception: figuring out how far away things are
Problem: fundamental ambiguity between size and distance.
visual
angle
Large pizza, far away?
Depth Perception: figuring out how far away things are
Problem: fundamental ambiguity between size and distance.
visual
angle
… or small pizza, close by?
• Retinal signal is the same in both cases
• Have to use a variety of “cues” to decide distance to things
Moon illusion: moon looks bigger at horizon than at its zenith
One explanation:
•
moon subtends same visual angle at horizon as at zenith (0.52 deg = a thumb!s
width an arm!s length)
• could be that “sky” overhead is perceived as being closer than sky at horizon
• therefore, people infer that the overhead moon must be smaller
Motivating questions:
1. Why do we have two eyes?
2. How does the brain combine
information from the two eyes to get
a percept of depth?
3. How can information from just one
eye provide a percept of depth?
Why have two eyes?
1. Binocular summation: pool twice as much light.
– (Eye chart is easier to read with both eyes than with one, for example)
2. Increase field of view (prey, more than predators)
110 deg
binocular
360 deg vision!
190 deg total
Why have two eyes?
1. Binocular summation: pool twice as much light.
– (Eye chart is easier to read with both eyes than with one, for example)
2. Increase field of view (prey, more than predators)
“This explains why it is so hard
to sneak up on a rabbit.”
360 deg vision!
Why have two eyes?
1. Binocular summation: pool twice as much light.
– (Eye chart is easier to read with both eyes than with one, for example)
2. Increase field of view (prey, more than predators)
3. Depth perception: can tell how far away things are
by comparing the images captured by two eyes
But first…
• Monocular depth cue: cue that is
available even when the world is viewed
with one eye alone
(Perhaps surprisingly, you can get an awful lot of info about
depth from just a single eye!)
Monocular Cues to Three-Dimensional Space
Occlusion: one object obstructs the view of part of
another object
• cue to relative depth order
• non-metrical depth cue - provides order information
only, no measure of distance in depth
Monocular Cues to Three-Dimensional Space
Occlusion: one object obstructs the view of part of
another object
could be accidental view of this
more likely scene
Relative Size
Metrical depth cue:
A depth cue that
provides
quantitative
information about
distance in the third
dimension
If all beads are all the
same size, then a bead
twice as small is twice as
far away
Depth from Shadows
Depth from Shadows
Texture Gradient
Size, Texture Gradient, & Height in Plane
Size & Texture = less influential if not paired
with Height in Plane
Rabbits on a wall?
Height in plane & “Haze”
higher, hazier
farther
Linear perspective
• parallel lines converge if moving away in depth
• this is due to perspective projection
Medieval (pre-renaissance) art
renaissance art
anamorphic projection
Use rules of linear
perspective to create
an image that appears
3D only from a
particular vantage point
(same idea used in street art)
Hans Holbein, The Ambassadors (1533)
Motion Parallax
• Nearby objects move by more quickly than far away objects
Demo: programming a video display to give parallax
depth cues using the wii-mote. (Johnny Lee)
http://www.youtube.com/watch?v=Jd3-eiid-Uw
Accommodation - “depth from focus”
near
far
• Lens needs more accommodation to focus nearby objects
Summary of Monocular Depth Cues:
Pictorial
• occlusion
• relative size
• shadow
• texture gradient
• height in plane
• linear perspective
Non-Pictorial
• motion parallax
• accommodation
(depth from focus)
Next up: binocular depth cues!
• Binocular depth cue: A depth cue that
relies on information from both eyes
Two Retinae Capture Different images
Finger-Sausage Illusion:
Binocular depth cues:
1. Vergence angle - angle between the eyes
If you know the
angles of the two
eyes, you can
deduce the distance
to the fixation point
Binocular depth cues:
2. Binocular Disparity - difference between two retinal images
We!ll spend some time on this one...
Stereopsis - depth perception that results from binocular
disparity information
(This is what they!re offering at IMAX 3D movie showings...)
Pen Test:
Hold a pen out at half
arm!s length
With the other hand,
see how rapidly you
can place the cap on
the pen.
First using two eyes,
then with one eye
closed
Retinal images in left & right eyes
Figuring out the depth from these two images is a challenging
computational problem. (Can you reason it out?)
Horopter: set of points in space that fall on
the retina at zero disparity
(i.e., they land on corresponding parts of the
two retinae)
A bit of geometric
reasoning will convince
you that this surface is a
circle containing the
fixation point and the two
eyes
point with
uncrossed
disparity
point with
crossed
disparity
appears closer
appears further
Is this a simple picture or a
complicated computational problem?
Interpreting the visual information
from three circles
This one requires
an accidental
viewpoint
Known as the “correspondence problem” - which points
in the left eye go with which points in the right eye?
Wheatstone!s stereoscope
Free fusing - focusing the eyes either nearer or farther than
this image so that each eye sees a different image
Free fusing - focusing the eyes either nearer or farther than
this image so that each eye sees a different image
“Crossed-fusion”
L retina
R retina
Free fusing - focusing the eyes either nearer or farther than
this image so that each eye sees a different image
“uncrossed fusion”
L retina
R retina
Random Dot Stereogram - same concept, but no
detectable “features” in either image. Details of dot pattern
allow brain to solve the correspondence problem
“Magic Eye” images use same principle